Bicubic spline smoothing of the data given at points of a rectangular network |
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Authors: | Věnceslava Pretlová Reviewer I P?en?ik |
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Institution: | (1) Institute of the Physics of the Atmosphere, Czechosl. Acad. Sci., Prague |
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Abstract: | Summary A computational method for fitting smoothed natural or periodic bicubic splines to data given at the grid points of a rectangular network is proposed. The one-dimensional smoothed spline fit, introduced by Reinsch, defines the smoothness properties well. These are generalized for a two-dimensional approximation by solving the corresponding variational problem. The defining equations are presented here together with an efficient method of determining the necessary parameters and computing the resultant spline.
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a![ubreve](/content/g4l6542088211835/xxlarge365.gif) a u, n![iecy](/content/g4l6542088211835/xxlarge1077.gif) u ¶rt;u![chcy](/content/g4l6542088211835/xxlarge1095.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) ![scy](/content/g4l6542088211835/xxlarge1089.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) ![scy](/content/g4l6542088211835/xxlarge1089.gif) u u ¶rt;![ncy](/content/g4l6542088211835/xxlarge1085.gif) ![ocy](/content/g4l6542088211835/xxlarge1086.gif) an a![vcy](/content/g4l6542088211835/xxlarge1074.gif) ![lcy](/content/g4l6542088211835/xxlarge1083.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) uu. ![rcy](/content/g4l6542088211835/xxlarge1088.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) ![zcy](/content/g4l6542088211835/xxlarge1079.gif) ![ucy](/content/g4l6542088211835/xxlarge1091.gif) ![lcy](/content/g4l6542088211835/xxlarge1083.gif) mam ![vcy](/content/g4l6542088211835/xxlarge1074.gif) ![ycy](/content/g4l6542088211835/xxlarge1099.gif) 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![yacy](/content/g4l6542088211835/xxlarge1103.gif) ![vcy](/content/g4l6542088211835/xxlarge1074.gif) ![ncy](/content/g4l6542088211835/xxlarge1085.gif) ![ocy](/content/g4l6542088211835/xxlarge1086.gif) ![fcy](/content/g4l6542088211835/xxlarge1092.gif) ![ocy](/content/g4l6542088211835/xxlarge1086.gif) ![rcy](/content/g4l6542088211835/xxlarge1088.gif) ![mcy](/content/g4l6542088211835/xxlarge1084.gif) . ![Dcy](/content/g4l6542088211835/xxlarge1044.gif) ![lcy](/content/g4l6542088211835/xxlarge1083.gif) n a mu![chcy](/content/g4l6542088211835/xxlarge1095.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) ![scy](/content/g4l6542088211835/xxlarge1089.gif) u ![vcy](/content/g4l6542088211835/xxlarge1074.gif) ![ycy](/content/g4l6542088211835/xxlarge1099.gif) u![scy](/content/g4l6542088211835/xxlarge1089.gif) ![lcy](/content/g4l6542088211835/xxlarge1083.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) u ![bcy](/content/g4l6542088211835/xxlarge1073.gif) ![ycy](/content/g4l6542088211835/xxlarge1099.gif) a o ma![vcy](/content/g4l6542088211835/xxlarge1074.gif) ![lcy](/content/g4l6542088211835/xxlarge1083.gif) ![iecy](/content/g4l6542088211835/xxlarge1077.gif) a n![rcy](/content/g4l6542088211835/xxlarge1088.gif) ![ocy](/content/g4l6542088211835/xxlarge1086.gif) ![gcy](/content/g4l6542088211835/xxlarge1075.gif) a![mcy](/content/g4l6542088211835/xxlarge1084.gif) a a ![yacy](/content/g4l6542088211835/xxlarge1103.gif) ![zcy](/content/g4l6542088211835/xxlarge1079.gif) ![ycy](/content/g4l6542088211835/xxlarge1099.gif) ![kcy](/content/g4l6542088211835/xxlarge1082.gif) FORTRAN.
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